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<p><dfn class="terminology">Theorem</dfn> Suppose that <span class="process-math">\(P_1(x), P_2(x), \cdots, P_n(x)\)</span> are continuous on an open interval <span class="process-math">\(I\text{.}\)</span> If <span class="process-math">\(W(y_1, y_2, \cdots, y_n)\)</span> is not equal to zero at a point <span class="process-math">\(x_0\)</span> in <span class="process-math">\(I\)</span> (it can be shown that this implies <span class="process-math">\(W(y_1, y_2, \cdots, y_n) \neq 0\)</span> on the whole interval). Then (<a href="" class="xref" data-knowl="./knowl/eq4_3.html" title="Equation 4.1.4">(4.1.4)</a>) is the general solution and <span class="process-math">\(y_1, y_2, \cdots, y_n\)</span> are then called a fundamental set of solutions.</p>
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